Anthony Cumia's tweeted his outrage at a woman he said punched him in the face on a New York street

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In this file photo, radio shock jocks Greg "Opie" Hughes, left, and Anthony Cumia, right, leave CBS Radio studios on 57th Street on Wednesday, April 26, 2006, in New York

Radio talk show host Anthony Cumia is offering no apologies for what satellite radio company SiriusXM called a hate-filled Twitter rant that got him fired.

The former co-host of the "Opie & Anthony" show was let go July 3 after tweeting his outrage at a woman he said punched him in the face on a New York street. Cumia responded in an interview early Saturday on Fox News' "Red Eye."

His tweets used an expletive degrading to women, and SiriusXM called them "racially charged." The woman he encountered is black.

He says he used words like "animal" and "savage" to describe people who resort to violence, not people of a certain race.

"People who listened to me on the air would have known, 'Yeah, he talks like that on the show all the time,'" Cumia told Fox. "For 10 years at SiriusXM, I had spoken like that, stringing together lines of obscenities in nonsensical fashion."

He said he believed no one had approached SiriusXM to say he should be fired.

"It was such a kneejerk reaction in this day and age," he said, adding, "I will never apologize for this. ... I didn't do anything wrong."